Question

4. Two friends are playing a matching card game where friend 1, Max, chooses an Ace, Two, or Three and friend 2, Lucy, plays King, Queen, or Jack. Depending on what cards they play, they split the pot differently. The payoffs are summarized in the following table: (3.3) Lucy King Queen Jack Ace (4,1) (1,2) (3.2) Max Two (3.2) (2.1) Three (1,1) (1.2) (4,4) (a) Use iterated elimination of strictly dominated actions (IESDA) to eliminate actions for Max and Lucy. Write out which action is dominated and HOW it is dominated (if you use a mixed strategy to eliminate another action, you need to specify the set of possible mixes or a particular mix). (8 points) 6 (b) Write out the definition of Nash Equilibrium, then solve for all Nash Equilibrium/Equilibrin of the (reduced) game. Circle your answer. (8 points)

Answer 1

when Max chooses two, Lucy will choose Queen as 3 > 1, when Lucy chooses Queen, Max will choose Two as 3 > 1.

Again, when Max chooses Three ,Lucy will choose Jack as 4 >2 and when Lucy chooses Jack, Max will choose Three as 4 >2.